Biot slow‐wave effects in stratified rock

Abstract

The transmission of P‐waves through the stratified layers of a sedimentary basin is modeled numerically using Biot theory. The effects on the transmissivity of frequency, angle of incidence, layer thickness, permeability and elastic compliance of the rocks are all considered. Consistent with previous analytical work, it is found that the equilibration of fluid pressure between the fine layers of a sedimentary sequence can produce significant P‐wave attenuation at low frequencies. For this attenuation mechanism to act within the surface‐seismic band (say, 3–300 Hz), we find that there must be layering present at the scale of centimeters to tens of centimeters. If the layering is restricted to layers of roughly 1 m thickness or greater, then for typical sandstone formations, the attenuation caused by the interlayer flow occurs below the seismic band of interest. Such low‐frequency interlayer flow is called Biot slow‐wave diffusion in the context of Biot theory and is likely to be the dominant source of low‐frequency attenuation in a sedimentary basin, even for relatively tight and stiff reservoir rock; however, the effect is enhanced in more compliant materials. At higher frequencies, the generation of slow‐waves at interfaces is also shown to significantly affect the P‐wave scattering so long as the layers are sufficiently thin and sufficiently compliant. This effect on the P‐wave scattering is shown to increase with increasing angle of incidence. Our work is limited to performing numerical experiments, with care given to making realistic estimates of all the material properties required. No attempt is made here to define an equivalent viscoelastic solid that allows for such slow‐wave effects.